arXiv subjects

Ahmed Al-Shujary

Publications and source records attributed to Ahmed Al-Shujary.

3 recordsLinked to original sources

arXiv2019

On moduli spaces of Kähler-Poisson algebra over rational functions in two variables

Kähler-Poisson algebras were introduced as algebraic analogues of function algebras on Kähler manifolds, and it turns out that one can develop geometry for these algebras in a purely algebraic way. A Kähler-Poisson algebra consists of a Poisson algebra together with the choice of a metric structure, and a natural question arises: For a given Poisson algebra, how many different metric structures are there, such that the resulting Kähler-Poisson algebras are non-isomorphic? In this paper we initiate a study of such moduli spaces of Kähler-Poisson algebras defined over rational functions in two variables.

math.RA↗

arXiv2019

Morphisms, direct sums and tensor products of Kähler-Poisson algebras

In this paper we introduce the concept of morphisms of Kähler-Poisson algebras and study their algebraic properties. In particular, we find conditions, in terms of the metric, for two algebras to be isomorphic, and we introduce direct sums and tensor products of Kähler-Poisson algebras. We provide detailed examples to illustrate the novel concepts.

math.RA↗

arXiv2017

Kähler-Poisson algebras

We introduce Kähler-Poisson algebras as analogues of algebras of smooth functions on Kähler manifolds, and prove that they share several properties with their classical counterparts on an algebraic level. For instance, the module of inner derivations of a Kähler-Poisson algebra is a finitely generated projective module, and allows for a unique metric and torsion-free connection whose curvature enjoys all the classical symmetries. Moreover, starting from a large class of Poisson algebras, we show that every algebra has an associated Kähler-Poisson algebra constructed as a localization. At the end, detailed examples are provided in order to illustrate the novel concepts.

math.RA↗